Mathematical physics, including mathematics, is a research area where novel mathematical techniques are invented to tackle problems in physics, and where novel mathematical ideas find an elegant physical realization. Historically, it would have been impossible to distinguish between theoretical physics and pure mathematics. Often spectacular advances were seen with the concurrent development of new ideas and fields in both mathematics and physics. Here one might note Newton's invention of modern calculus to advance the understanding of mechanics and gravitation. In the twentieth century, quantum theory was developed almost simultaneously with a variety of mathematical fields, including linear algebra, the spectral theory of operators and functional analysis. This fruitful partnership continues today with, for example, the discovery of remarkable connections between gauge theories and string theories from physics and geometry and topology in mathematics.
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Homological Link Invariants from Floer Theory
Elise LePage University of California, Berkeley

Higher Weyl modules, coinvariants, and factorization homology
Maciej Szczesny Boston University

Quantum matter from algebraic geometry
Steven Rayan University of Saskatchewan

Quiver algebras and their representations for arbitrary quivers
Wei Li Chinese Academy of Sciences

Chromatic aberrations of the geometric Satake equivalence
Sanath Devalapurkar Harvard University

Quantum groups, clusters, and Hamiltonian reduction
Alexander Shapiro University of Edinburgh

Integrable systems from CalabiYau categories
Nick Rozenblyum University of Chicago

Nonvectorbundle Thom spectra and applications to anomalies
Arun Debray University of Texas  Austin

Decategorifying the singular support of coherent sheaves
Kendric Schefers The University of Texas at Austin

On HikitaNakajima conjecture for some quiver varieties and Slodowy slices
Vasily Krylov Massachusetts Institute of Technology (MIT)

VOAs and Twisted ChernSimons Matter Theories
Niklas Garner University of Washington